In this paper, we consider the usual Lucas numbers and the generalized order-k Fibonacci numbers. Then we give a new definition for generalization of the Lucas numbers. Therefore, we give the ...

https://doi.org/10.4169/college.math.j.48.2.97 https://www.jstor.org/stable/10.4169/college.math.j.48.2.97 Hong recently explored when the value of the generating ...

Learn about the origins of the Fibonacci sequence, its relationship with the golden ratio and common misconceptions about its significance in nature and architecture. When you purchase through links ...

A variation of a puzzle called the “pick-up sticks problem” asks the following question: If I have some number of sticks with random lengths between 0 and 1, what are the chances that no three of ...

An unusual arrangement of leaves in a 407-million-year-old fossilized plant is complicating scientists’ understanding of plant evolution. Most land plants living today have spiral patterns involving ...

Liverpool FC's victory at the weekend has clinched them their second Premier League title but it also resulted in something curious – producing a strange series of numbers in the league's record books ...